From: Matt Mahoney (matmahoney@yahoo.com)
Date: Thu Jan 24 2008 - 09:57:08 MST
--- Vladimir Nesov <robotact@gmail.com> wrote:
> On Jan 24, 2008 3:38 AM, Matt Mahoney <matmahoney@yahoo.com> wrote:
> >
> > --- Vladimir Nesov <robotact@gmail.com> wrote:
> >
> > > On Jan 23, 2008 11:52 PM, Matt Mahoney <matmahoney@yahoo.com> wrote:
> > > >
> > > >
> > > > An example of uncomputable phenomena would be something like classical
> > > > mechanics, in which the outcome of an experiment requires knowledge of
> the
> > > > position and velocity of particles with infinite precision.
> > >
> > > Again: how would you test that?
> >
> > We would not have probabilistic theories of physics like quantum
> mechanics.
>
> What _would_ we have then? Absence of certain _theory_ hardly tells
> anything.
We could have laws of physics that allow us to make exact predictions. The
existence of any such law would prove that the universe is not simulated.
>
> > > > > Finite state machine can perfectly well simulate itself, in any
> > > > > natural interpretation that comes to mind (you'd have to
> additionally
> > > > > define what it means for this formal construct to have a simulation
> of
> > > > > something).
> > > >
> > > > A finite state machine with n states cannot model a machine with more
> than
> > > n
> > > > states.
> > >
> > > Not every machine, but who needs that? And again, what do you mean by
> > > modeling?
> >
> > If machine A simulates machine B, you could not run a program on B that
> > simulates A. It would not have enough memory.
> >
>
> You keep telling that. But it's a simple question of validity of
> theorem on mathematical model. Define mathematically your assertion.
>
> You can simulate machine B of googleplex states which doesn't do
> anything on a 1-state machine which also doesn't do anything.
I mean that if there is a program on A that can simulate any program on B,
then there is no program on B that could simulate this program on A. I could
make a similar argument about Turing machines, replacing the number of states
with algorithmic complexity. In either case, it means you cannot build a
computer that could run an exact simulation of the universe (including your
computer), unless the universe is not computable by a Turing machine.
>
>
> > > > > > 2. The universe has finite entropy. It has finite age T, finite
> size
> > > > > limited
> > > > > > by the speed of light c, finite mass limited by G, and finite
> > > resolution
> > > > > > limited by Planck's constant h. Its quantum state can be
> described in
> > > > > roughly
> > > > > > (c^5)(T^2)/hG ~ 2^404.6 ~ 10^122 bits. (By coincidence, if the
> > > universe
> > > > > is
> > > > > > divided into 10^122 parts, then one bit is the size of the
> smallest
> > > stable
> > > > > > particle, even though T, c, h, and G do not depend on the
> properties
> > > of
> > > > > any
> > > > > > particles).
> > > > >
> > > > > So? If anything, it supports knowability of universe, a counterpart
> of
> > > > > it being simulated from complex unobservable environment.
> > > >
> > > > Yes, that is my point.
> > >
> > > Well, I meant 'counterpart' as in 'opposite'. Problem with simulated
> > > worlds is (supposedly) that complex unpredicatable miracles can
> > > happen. If everything is simple and observable, what is the problem?
> > > 'Simulatedness' is not observable and in itself is a meaningless
> > > category.
> >
> > AIXI makes complex or unusual events unlikely.
>
> AIXI doesn't 'make' anything, it's not even an applied theory.
AIXI proves the optimal strategy of an intelligent agent. It says you would
be smart to assume the universe is simple.
> > > How would you test if your notion of Occam's razor didn't work?
> >
> > Occam wouldn't have made the observation, and physicists would not keep
> trying
> > to make their theories simple and elegant.
>
> Maybe Occam wouldn't had existed. It's not exactly a test.
Not exactly, but I don't claim to have a proof that the universe is simulated.
> > > > The fastest way to find a universe supporting intelligent life is run
> the
> > > k'th
> > > > universe for k steps. I claim that for our universe, k ~ 10^122.
> > >
> > > But how does it relate to complexity of laws of physics which are much
> > > simpler?
> >
> > The k'th universe will have complexity log(k), which is what we actually
> > observe (very roughly).
>
> Ah, you attribute complexity of content to runtime, as per MWI that
> starts with low complexity and obtains its current complexity given
> enough time. Did I get that right? Interesting.
Yes, about 10^244 steps to be exact.
-- Matt Mahoney, matmahoney@yahoo.com
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